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We apply the Deloye & Bildsten (2003) isentropic models for donors inultracompact low-mass X-ray binaries to the AM CVn population of ultracompact,interacting binaries. The mass-radius relations of these systems' donors in themass range of interest ($M_2<0.1 \msun$) are not single-valued, butparameterized by the donor's specific entropy. This produces a range in therelationships between system observables, such as orbital period, $\Porb$, andmass transfer rate, $\Mdot$. For a reasonable range in donor specific entropy,$\Mdot$ can range over several orders of magnitude at fixed $\Porb$. Wedetermine the unique relation between $\Mdot$ and $M_2$ in the AM CVn systemswith known donor to accretor mass ratios, $q=M_2/M_1$. We use structuralarguments, as well as each system's photometric behavior, to place limits on$\Mdot$ and $M_2$ in each. Most systems allow a factor of about 3 variation in$\Mdot$, although V803 Cen, if the current estimates of its $q$ are accurate,is an exception and must have $M_2 \approx 0.02 \msun$ and $\Mdot \approx10^{-10} \msun$ yr$^{-1}$. Our donor models also constrain each donor's coretemperature, $T_c$, range and correlate $T_c$ with $M_2$. We examine howvariations in donor specific entropy across the white dwarf family\citep{nele01a} of AM CVn systems affects this population's current galacticdistribution. Allowing for donors that are not fully degenerate produces ashift in systems towards longer $\Porb$ and higher $\Mdot$ increasing theparameter space in which these systems can be found. This shift increases thefraction of systems whose $\Porb$ is long enough that their gravity wave (GW)signal is obscured by the background of detached double white dwarf binariesthat dominate the GW spectrum below a frequency $\approx 2$ mHz.Comment: 13 pages, 10 figures, uses emulateapj.cls. Accepted to Astrophysical  Journa

Arbitrarily Degenerate Helium White Dwarfs as Donors in AM Canum Venaticorum Binaries